Kobayashi, Toshiyuki Branching problems of unitary representations. (English) Zbl 1008.43009 Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20-28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press. 615-627 (2002). Basic theory and new perspectives of admissible restrictions are presented from both the analytic and the algebraic point of view, such as:1. Admissible restrictions to subgroups, including a criterion for admissible restrictions and its converse statement;2. infinitesimal discrete decomposability, including a discrete branching law, a criterion for discrete decomposability and the size of irreducible summands;3. some applications to representation theory;4. new discrete series for homogeneous spaces, nonsymmetric spaces, symmetric spaces and an exclusive law of discrete spectrum for restriction and induction;5. modular varieties and vanishing theorems, including vanishing theorems for modular symbols.For the entire collection see [Zbl 0993.00022]. Reviewer: Su Weiyi (Nanjing) Cited in 2 ReviewsCited in 9 Documents MSC: 43A85 Harmonic analysis on homogeneous spaces 22E46 Semisimple Lie groups and their representations 11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53D20 Momentum maps; symplectic reduction Keywords:admissible restrictions; infinitesimal discrete decomposability; discrete branching law; discrete series; modular varieties; vanishing theorems PDFBibTeX XMLCite \textit{T. Kobayashi}, in: Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20--28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press; Singapore: World Scientific/distributor. 615--627 (2002; Zbl 1008.43009) Full Text: arXiv